Estimating uncertainties in the back-mapping of the fast solar wind

¹ Centre for mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
² Solar-Terrestrial Centre of Excellence, Royal Observatory of Belgium, Avenue Circulaire 3, B-1180 Brussels, Belgium
³ Columbia Astrophysics Laboratory, Columbia University, MC 5247, 550 West 120th Street, New York, NY 10027, USA

^⋆ Corresponding author; alexandros.koukras@columbia.edu

Received: 23 June 2022
Accepted: 16 November 2024

Abstract

Context. Although the most likely source regions of fast solar wind relate to coronal holes, the exact acceleration mechanism that drives the fast solar wind is still not fully understood. An important approach that can improve our understanding involves the combination of remote sensing and in situ measurements, often referred to as linkage analysis. This linkage tries to identify the source location of the in situ solar wind with a process called back-mapping. Typically, back-mapping is a combination of ballistic mapping, where the solar wind draws the magnetic field into the Parker Spiral at larger radial distances, and magnetic mapping, where the solar wind follows the magnetic field line topology from the solar surface to a point in the corona where the solar wind starts to expand radially.

Aims. By examining the different model ingredients that can affect the derived back-mapped position, we aim to provide a more precise estimate of the source location and a measure of confidence in the mapping procedure. This can be used to improve the connection between remote sensing and in situ measurements.

Methods. For the ballistic mapping, we created velocity profiles based on Parker wind approximations. These profiles are constrained by observations of the fast solar wind close to the Sun and are used to examine the mapping uncertainty. The coronal magnetic field topology from the solar surface up to an outer surface (the source surface) radius R_SS is modeled with a potential field source surface extrapolation (PFSS). As inputs, the PFSS takes a photospheric synoptic magnetogram and a value for the source surface radius, where this latter is defined as the boundary after which the magnetic field becomes radial. The sensitivity of the extrapolated field is examined by adding reasonable noise to the input magnetogram and performing a Monte Carlo simulation, where we calculate the source position of the solar wind for multiple noise realizations. Next, we examine the effect of free parameters –such as the height of the source surface– and derive statistical estimates. We used Gaussian Mixture clustering to group the back-mapped points associated with different sources of uncertainty, and provide a confidence area for the source location of the solar wind. Furthermore, we computed a number of metrics to evaluate the back-mapping results and assessed their statistical significance by examining three high-speed stream events. Finally, we explored the effect of corotation close to the Sun on the derived source region of the solar wind.

Results. For back-mapping with a PFSS corona and ballistic solar wind, our results show that the height of the source surface produces the largest uncertainty in the source region of the fast solar wind, followed by the noise in the input magnetogram, and the choice of the velocity profile. Additionally, we display the ability to derive a confidence area on the solar surface that represents the potential source region of the in situ-measured fast solar wind.